The application describes both parametric and non-parametric approaches to modeling the impact of baseline or time-varying covariates (both low- and high-dimensional) on repeated measures of important biomarker outcomes. Our first aim considers parametric approaches to modeling virological or immunological response to treatment. To be useful, such models must be flexible enough to allow abrupt as well as gradual changes in marker trajectories, and must also incorporate of the impact of factors such as accumulation of resistance mutations, host responses, treatment changes and consequences of co-infections. The models must also accommodate uncertainty in the nature and timing of events, like development of mutations, which cause such changes, as well as frequently missing data. Modeling the effect of resistance is made challenging by the large number of possible mutations and interactions among these mutations, as well as by the presence of multiple clades of virus, large numbers of possible treatments, and the variety of treatment response is measured. Non-parametric methods like CART are available to help reduce the dimensionality of genetic data, and therefore suggest variables for inclusion in parametric models, like those described above. We propose extending CART methodology to allow for both genetic sequences and viral load measurements that are repeated over time, and consider both parametric and non-parametric longitudinal models. Our second aim considers a resampling- based approach to analyze the effect of baseline genetic sequences that is fully nonparametric and allows arbitrary times of measurement. The third aim uses resampling-based methods to test whether variations in the best tree over time are (using the repeated sequences) are consistent with constant underlying relationships between resistance mutations and treatment outcomes, or instead imply that relationships change over time. Our final aim develops non-parametric methods for relating high-dimensional predictors, like HIV genotype or host genetic SNPs, to correlations between responses of interest, possibly with adjustment for other covariates. The goal is to identify predictors of discordance among markers in response to treatment. PUBLIC HEALTH RELEVANCE: The application describes both parametric and non-parametric approaches to describing the impact of baseline or time-varying covariates (both low- and high-dimensional) on repeated measures of important outcomes like viral load or measures of immune function. Challenges arise from the fact that abrupt changes can occur in longitudinal biomarker processes from events like development of resistance mutations whose exact timing is unobservable, as well as from the high dimensionality of the viral genotype and the presence of different types of censoring. Our proposed methods include both highly flexible longitudinal models that accommodate uncertain timing of viral rebound or development of mutations, and non-parametric exploratory methods that accommodate repeated measures of both genotype and viral load;not only does the latter permit investigation of the relationship between patterns of resistance mutations and responses to treatment, but also of the evolution of that relationship over time.